A number of loan players will depart with some of the club's star players likely to interest clubs from England and around Europe. There has been talk of a director of football being brought to the club, something talked up by former boss Brendan Rodgers.
John Kennedy, who worked under Rodgers and then Neil Lennon, is currently in interim charge and won his first game at the weekend, defeating Aberdeen 1-0 at Celtic Park.
Many Celtic fans will be looking for a more prestigious name to be appointed and there have been some big names touted who will bring a variety of styles to the club.
Scroll down and click through for the latest odds supplied by Betfair on the most likely candidates to replace Neil Lennon permanently.
17. John Kennedy - 4/1
The former centre-back has taken interim charge since Neil Lennon's departure and led the team to a 1-0 win over Aberdeen on Saturday. Photo: Craig Williamson - SNS Group
18. Eddie Howe - 10/3
Even before Lennon had left, Howe was a strong contender to be the next Celtic boss. Photo: Jordan Mansfield